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If $a + b + c = 0,$ then $a^{3} + b^{3} + c^{3} =$

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$- 3$ abc

3abc

6abc

answer is C.

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Detailed Solution

$a + b + c = 0 \Rightarrow a + b = - c$

Cubing on both sides

${(a + b)}^{3} = {(- c)}^{3}$

$a^{3} + b^{3} + 3 a b (a + b) = - c^{3}$

$a^{3} + b^{3} + 3 a b (- c) = - c^{3}$

$a^{3} + b^{3} + c^{3} = 3 a b c$

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